Since then, Davie's work has led to a certain number of results in several directions which are usually done in the additive cases. One can take \(w\)  to be a more general stochastic process and still has (even better) regularization by noise phenomenon. For example one can consider \(w\)  to be a fractional Brownian motion [1]}, a Lévy process, see [2]}, [3]} and the references therein, or a more general stochastic process [4]}, [5]}, [6]}.
In a more general context some similar results when \(w\)  is non random and as general as possible can be exhibited [7]}, [1]} and [9]}, [10]}.
This phenomenon of regularization by noise in a path-by-path manner was also study in other kind of problems, such as SPDEs [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, mean field differential equations [17]}, [18]}, and in a mixed additive/multiplicative setting [19]}, [20]}.
